Cairo (CNN) -- Egypt's first democratically elected president moved into his offices Monday and began the work of putting together a government, an adviser to the transition team told CNN.
President-elect Mohamed Morsi is picking people to serve in his Cabinet, but the process is deliberate and "won't end in a day," said Jihad Haddad, the adviser.
Euphoric jubilation spilled into a second day Monday in Cairo's Tahrir Square, where revelers celebrated Morsi's election. But with the hopes of the Egyptian revolution resting on his shoulders, the former Muslim Brotherhood member faces an array of challenges both at home and abroad.
For the moment, the presidency is largely a figurehead position as Egypt's Supreme Council of the Armed Forces maintains widespread control over the country -- just as it has since Hosni Mubarak's 30-year rule succumbed to a popular revolt last year.
Monday, the president-elect met with top SCAF leaders, according to state-run media and sources within the Freedom and Justice Party, the political arm of the Muslim Brotherhood.
Under an interim constitutional declaration, the military council said it retains the power to make laws and budget decisions until a new constitution is written and a new parliament is elected.
Though some shed tears of joy after Morsi's historic win, others remained skeptical about what the victory really means.
"(Morsi) doesn't have the power -- SCAF has the power," a young man named Mohamed Saleh said.
But in his first speech since defeating former Prime Minister Ahmed Shafik, Morsi said he is "in charge," while also stressing he must answer to the people.
"We are all equal in rights, and we all have obligations to carry on for this country," he said Sunday night. "As for myself, I have no rights, but I have obligations."
The longtime Muslim Brotherhood member paid special tribute to the "martyrs" from the revolution that led to Mubarak's ouster in February 2011 and, more than a year later, to Morsi's election.
"This blood will not go in vain," Morsi said.
Earlier in the day, election officials announced Morsi earned more than 13 million votes in last week's presidential election, while Shafik -- the last prime minister to serve under Mubarak -- had more than 12 million. That worked out to just under 52% of the vote for Morsi, while Shafik got just over 48%, officials said.
The victory triggered massive cheers and celebratory gunfire in Cairo's Tahrir Square, the hub of last year's revolution.
"We've been waiting for it for 7,000 years," said Abdul Mawgoud Dardery, a member of the Muslim Brotherhood's Freedom and Justice Party. "For the first time in history, we have our own president, elected by us."
But some Shafik supporters were crushed by the news. Manal Koshkani said she and others fear the direction the Muslim Brotherhood could take Egypt.
"I hope we see a better future," Koshkani said. "I highly doubt it."
Shortly after defeating Shafik, Morsi resigned from the Muslim Brotherhood and its Freedom and Justice Party and vowed to represent all Egyptians.
But Morsi inherits a struggling economy, with widespread poverty, high unemployment, and Egypt's vaunted tourism sector still sagging on the heels of the political unrest.
His victory also raised questions about Egypt's relations with Israel. Morsi didn't directly address Israel in his speech Sunday, though he did say "we will preserve all national and international agreements."
He previously told CNN he'd honor Egypt's 1979 accord with Israel, but in the past, the Islamist figure has referred to Israeli leaders as "vampires."
Israeli Prime Minister Benjamin Netanyahu said in a statement Sunday that "Israel appreciates the democratic process in Egypt and respects the results of the presidential elections. Israel looks forward to continuing cooperation with the Egyptian government on the basis of the peace treaty between the two countries, which is a joint interest of both peoples and contributes to regional stability."
Meanwhile, prominent Palestinian legislator Hanan Ashrawi said Palestinians "look for future cooperation with Egypt and its supportive position for the Palestinian cause."
Leaders from the country, region and world sent in their congratulations.
They included Egypt's Grand Mufti Ali Gomaa and the head of the Al Azhar religious authority, Ahmed al-Tayeb, who both congratulated Morsi, according to state-run media. The two are key Muslim figures in the country who were appointed by Mubarak.
U.S. President Barack Obama called Morsi to congratulate him and pledge to "support Egypt's transition to democracy and stand by the Egyptian people as they fulfill the promise of the revolution."
Earlier, the White House issued a statement calling on Morsi "to take steps at this historic time to advance national unity by reaching out to all parties and constituencies," including respecting the rights of women and religious minorities such as Coptic Christians.
Others described Morsi's election as momentous, but stressed that it doesn't mean the county's "revolution" or its problems are over.
Wael Ghonim, a former Google executive who helped organize the 2011 revolution, posted on Twitter: "The first elected civilian Egyptian president in the history of modern Egypt. The revolution continues."
CNN's Ben Wedeman, Dan Rivers, Holly Yan and journalists Mohamed Fadel Fahmy and Ian Lee contributed to this report.